The Wiener Index and Hyperbolic Geometry of Fullerene Graphs

We observe that fullerene graphs are one-skeletons of polytopes which can be realized in a hyperbolic 3-dimensional space with all dihedral angles equal to =2. We are referring volume of such polytope as a hyperbolic volume of a fullerene. We demonstrate that hyperbolic volumes of fullerenes correlate with few important topological indices and can serve as a chemical descriptor for fullerenes.